We apply, for the first time, the importance-truncation (IT) procedure based on the many-body perturbation theory for the multi-shell SU(3) scheme basis of the ab initio symmetry-adapted no-core shell model (SANCSM). It is shown that the IT method can yield a quantitative justification for the symmetry-based truncation of the SA-NCSM approach.
Furthermore, we demonstrate that the IT algorithm can be applied in a symmetry-truncated model space and it leads to even more dramatic reduction in dimensionality of the nuclear eigenvalue problem.